Assignment 2
Section 12.4
Problem 2:
Problem 8: The contour diagram in this problem does not represent a linear function.
Problem 10: the linear function is:
?
= 2
−
1
2
? −
2
3
?
Problem 18: A formula for
𝐵
is
𝐵
= 4.2 + 0.9
? −
120
+ 1.6
𝑠 −
8
The formula does not make sense for low weights or speeds. It means
𝐵
> 0
.
Problem 22: The formula for this linear function is
? ?
,
?
= 4 + 2
? − ?
Section 12.5
Problem 2: (a)(II)
(b)(I)
Problem 4:
?
2
+
?
2
+
?
2
= 4
Problem 12: Yes.
?
=
? ?
,
?
=
?
2
+ 3
?
2
Problem 22: since the square root function is nonnegative,
? ≥
0
. Setting
?
=
1
− ?
2
− ?
2
and
squaring both sides leads to
?
2
+
?
2
+
?
2
= 1
, which is the equation for a sphere of radius 1. The graph
of the function includes only those points where
? ≥
0
, that is, the upper hemisphere of radius 1,
centered at the origin.
If we take
? ?
,
?
,
?
=
? ?
,
? − ?
=
1
− ?
2
− ?
2
− ?
, then the level surface
? ?
,
?
,
?
= 0
is the
surface
𝑆
.
Problem 24:
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? −
1 =
− ?
2
+
?
2
This is the equation whose graph includes the desired cone. We express this equation as a level surface
? ?
,
?
,
?
= 1
− ?
2
+
?
2
− ?
= 0
.
Section 12.6
Problem 2: The function
1/(
?
2
+
?
2
)
is continuous on the square. The functions
?
2
and
?
2
are
continuous everywhere and so it their sum. The constant function1 is continuous, and thus so is the
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 Fall '08
 FORTMANN
 lim, Continuous function

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